# Refinements and Generalizations of the Shannon Lower Bound via Extensions of the Kraft Inequality

## TL;DR

This paper improves the Shannon lower bound in data compression by extending the Kraft inequality for various coding scenarios.

## Contribution

New extended versions of the Kraft inequality and refined Shannon lower bounds for different rate-distortion coding cases.

## Key findings

- Sharper bounds for one-to-one and D-semifaithful codes are derived.
- A Shannon lower bound for sliding-window distortion measures is established.
- An individual-sequence version of the Shannon lower bound is introduced.

## Abstract

We derive a few extended versions of the Kraft inequality for lossy compression, which pave the way to the derivation of several refinements and extensions of the well-known Shannon lower bound in a variety of instances of rate-distortion coding. These refinements and extensions include sharper bounds for one-to-one codes and D-semifaithful codes, a Shannon lower bound for distortion measures based on sliding-window functions, and an individual-sequence counterpart of the Shannon lower bound.

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Source: https://tomesphere.com/paper/PMC12840369